What is the sum of the series:-1/10 + 2/10^2 + 3/10^3.......to infinity ?

Hello student,
Please find the answer to your question below
Given series1/10 + 2/10^2 + 3/10^3.......to infinity
x + 2x^2 + 3x^3 + 4x^4 + ...
where x=1/10=0.1
this series is AGP where r=1/10 and a=1,d=1
=(a/1-r)+(dr/(1-r)²)
where a=1,d=1,r=0.1
=1.23456